Integers and Absolute Value
Think of the distance from one integer to another as being one step. If you start at zero and take two steps to the right, you get to 2. If you start at 0 and take two steps to the left, you get...
Real Numbers and Imaginary Numbers
Real numbers are what we get when we combine all the irrational and rational numbers. These numbers are "real" because they're useful for measuring things in the real world such as money, distan...
Fractions
What is a fraction?A fraction is a number written in the form , where q is nonzero. Any rational number can be written as a fraction. Fractions are usually used to think about "parts of a...
Equivalent Fractions
There are infinitely many different ways to represent the same fraction. Since we see no reason to abandon our brownie analogy, let's stick with it. Half of that pan of brownies can be represented...
Mixed Numbers
We've seen a bunch of examples of fractions so far, but what happens when we mix them up with whole numbers? As a quick reminder, a fraction whose numerator is smaller than its denominator is c...
Reducing Fractions
There are tons of ways to represent any one fraction. How do we choose which to use? It'll depend on the problem, but it's often helpful to simplify or reduce the fraction. We know that if we sta...
Comparing Fractions
Your Teacher May be a Complex Person, but She Likes Her Fractions SimplifiedAs you now know, there are infinitely many ways to express any particular fraction. Even more if you speak Spanish. Howev...
Multiplication and Division with Mixed Numbers
In order to multiply or divide with mixed numbers, turn the mixed numbers into fractions first. Just wave your wand over the top of them, whisper the magic incantation, and poof! Or, you can co...
Decimals
A decimal is another way of representing a real number. Many numbers that can be written as fractions can also be written as decimals, and vice versa. Sometimes it makes more sense to work with...
Percents
A percent is an abbreviation for a fraction where the denominator is 100. That fancy "%" sign means "over 100." So that 64% you got on your history pop quiz last week? Yeah, that wasn't actuall...
Things to Do with Real Numbers
Compare ThemWhen comparing real numbers, it can help to think of the number line. Ah, how fondly we remember it. Our favorite line of all the lines. The numbers on a number line get bigger as we go...
Decimals in Use
Paychecks and ExpensesSample ProblemLuis works 2.5 hours a day, 4 days a week. How many hours a week does Luis work?2.5 hours/day × 4 days/week = 10 hours/weekOnly 10 hours a week? Guess who...